show ambient occlusion in render output
The option in that menu is for the viewport only. To achieve the same effect in a cycles render you must either enable the setting in the world tab of the properties menu.

The best way to do this would be to enable an AO pass, which should be enabled by default.


You can then composite the AO pass with your image and control the effect after you've rendered. This is usually the node setup I use to control AO when compositing.